Nontrivial solutions for singular semilinear elliptic equations on the Heisenberg group

Abstract

In this article, we prove the existence of nontrivial weak solutions to the singular boundary value problemon the Heisenberg group. We employ Bonanno's three critical point theorem to obtain the existence of weak solutions.

Singular Adams inequality for biharmonic operator on Heisenberg Group and its applications

“…We point out that very little research works are available for the existence of solution to singular elliptic equations on Heisenberg group even for the Laplacian, see for instance [51,42,13]. For existence results related to Laplace equation without singularity, we refer to [8,9,10,11,14,28,27,29,30,36,37,38,39,52,53].…”

On the nonlocal Schrödinger‐poisson type system in the Heisenberg group

“…First, we would like to point out some of the important literatures related to our problem. For example, Tyagi 4 considered the singular boundary value problem in the Heisenberg group of the form: the existence of weak solutions are obtained by using the Bonanno's three critical point theorem. For critical case, An and Liu 5 obtained at least two positive solutions and a positive ground state solution to the following Schrödinger‐Poisson type system at 1 < q < 2: by the Green's representation formula and the critical point theory.…”

Uniqueness of positive solution for a quasilinear elliptic equation in heisenberg group

“…As for the p-sub-Laplacian case, Niu et al [7] considered the question of non-uniqueness of the (1.2) using the Picone Identity and the Pohozaev Identities for the p-sub-Laplacian on Heisenberg Group. Results on p-sub-Laplacian involving singular indefinite weight can be found in J.Dou [11] and J.Tyagi [1] and the reference therein. One of the biggest problem when dealing with p-sub-Laplacian is the nonavailability of the C 1,α regularity, although it has been proved in Marchi [12] to exist for p near 2.…”